The right to interest varies significantly from state-to-state and the type of action involved. Typically, in a contract action, interest would be payable from the date the debt was due. In an accident case, interest typically begins to run only after the judgment is entered.
The rate of interest would depend on the terms of your contract and/or your state's law. In accident cases, interest typically does not begin to run until the court enters a judgment in your favor.